Q Normal Distribution And The Application Of VaR Estimation In The Stock Market

The stock market is an important part of the financial market,its larger volatility and trading is the main part of the risk management. China’s stock market is still in the exploration stage.and it has many problems.For example,the method and technology of risk management methods is more backward,risk information disclosure system is not comprehensive and risk management system is not perfect. As the measure of risk is one of the mainstream methods,This paper is on the basis of some scholars.Firstly,it gives the theoretical basis of financial risk management and the traditional calculation method of value at risk.And it points out that the application of the VaR is necessary for the stock market of china.Secondly, it uses the theory of quantum calculus to derive probability density function of the corresponding q statistical distribution——q normal distribution;q exponential distribution and q uniform distribution, and the q normal distribution is applied to the calculation of VaR. This paper chooses daily logarithm data of shanghai composite index return as samples of the research. q normal distribution is applicable,and it is showed that daily logarithm data of shanghai composite index return obey the q normal distribution.Finally, q normal distribution is better compared with Tsallis q standard normal distribution.Our study reveals that the q normal distribution elucidates the properties of stock martet returns and is applicable to practical use of the VaR estimation.It solves fat tail of stock martet returns and the accuracy is improved.